We compare our cross-validation approaches \(\operatorname{CV}_{(1)}\)  (REF ), \(\operatorname{CV}_{\operatorname{mod}}\)  (REF ), and a 5-fold version of \(\operatorname{CV}_{(1)}\)  (see Appendix  and (REF ) in particular), all used with optimal partitioning, to a number of competitors. To this end, we use the functions CV1, CVmod, and VfoldCV from our R package crossvalidationCP, available on CRAN. To offer further flexibility, confer the documentation, it uses solely R code. If a fast implementation for a specialised setting is required, compliled code will be beneficial. The list of competitors include the \(\operatorname{COPPS}\)  procedure from [1]} described in Section REF , we use our own implementation given by the function COPPS in the R package crossvalidationCP; \(\operatorname{PELT}\)  [2]} and binary segmentation (\(\operatorname{BS}\) ) [3]}, both with the \(\operatorname{SIC}\) -penalty implemented in the R-package change-point; wild binary segmentation (\(\operatorname{WBS}\) ) [4]} with penalty \(1.3\)  times the \(\operatorname{SIC}\) -penalty implemented in the R-package wbs; \(\operatorname{SMUCE}\)  [5]} with a small error level \(\alpha = 0.05\)  as implemented in the R-package stepR; and \(\operatorname{FDRSeg}\)  [6]} with \(\alpha = 0.9\)  as implemented by the R-package FDRSeg. The latter two serve as representatives of more conservative and a more liberal procedures that control the family-wise error and \(\operatorname{FDR}\) -rate, respectively.
